Approximation relations on the posets of pseudometrics and of pseudoultrametrics

S. I. Nykorovych
2016 Karpatsʹkì Matematičnì Publìkacìï  
We show that non-trivial "way below" and "way above" relations on the posets of all pseudometrics and of all pseudoultrametrics on a fixed set X are possible if and only if the set X is finite.
doi:10.15330/cmp.8.1.150-157 fatcat:22ut2e7tp5fgxkqpkhxrtcy2im